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<p>We obtain weighted estimates in terms of the multilinear Fujii-Wilson constant introduced by Nieraeth (PhD thesis, Delft University of Technology (2020); arXiv preprint arXiv:2401.15725 (2024)) for multilinear fractional maximal function and multilinear fractional integral operators. Our Theorem 1.1 provides a positive answer to the conjecture posed in Nieraeth (Conjecture 3.3.6, PhD thesis, Delft University of Technology (2020)). Furthermore, the weighted estimates yield classical <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(A_{\vec {P},q}\)</EquationSource> </InlineEquation> estimates. In Lerner and Moen (Theorem 1.6, Studia Math. 219(3), 247–267 (2013)) and Cruz-Uribe and Moen (Theorem 2.5, Integral Equations Operator Theory 76(3), 421–446 (2013)), by means of extrapolation, the weighted estimates for multilinear Calderón-Zygmund operators and multilinear fractional integral operators were obtained. Without extrapolation we also provide the weighted estimates for multilinear fractional integral operators.</p>

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A note on weighted estimates for multilinear fractional integral operators

  • 期刊论文

  • 发表日期：

    2026年1月28日

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  • Li Zhang

摘要

We obtain weighted estimates in terms of the multilinear Fujii-Wilson constant introduced by Nieraeth (PhD thesis, Delft University of Technology (2020); arXiv preprint arXiv:2401.15725 (2024)) for multilinear fractional maximal function and multilinear fractional integral operators. Our Theorem 1.1 provides a positive answer to the conjecture posed in Nieraeth (Conjecture 3.3.6, PhD thesis, Delft University of Technology (2020)). Furthermore, the weighted estimates yield classical \(A_{\vec {P},q}\) estimates. In Lerner and Moen (Theorem 1.6, Studia Math. 219(3), 247–267 (2013)) and Cruz-Uribe and Moen (Theorem 2.5, Integral Equations Operator Theory 76(3), 421–446 (2013)), by means of extrapolation, the weighted estimates for multilinear Calderón-Zygmund operators and multilinear fractional integral operators were obtained. Without extrapolation we also provide the weighted estimates for multilinear fractional integral operators.